From the solid fabric, cut 16 strips 1″ x WOF. We will sub-cut as needed when we join the blocks.

Stack the 6 fat quarters aligning the edges. Trim and square the edges of the entire stack.

We will be making several cuts through the entire stack of 6 FQs. There are no measurements for the cuts. You may make the cuts anywhere in alternating directions to give it a balanced look

Make the first cut along the shorter (18″) side so that one side is slightly bigger than the other. My cut was approximately 2/3 from the left. This gives us two rectangles.

Make the next cut within each rectangle, perpendicular to the previous cut. Make sure the cuts on each side are staggered to give an unmatched look.

Make the next cut in some or all of the four rectangles above, perpendicular to the previous cut, making sure the cuts on adjacent rectangles do not match. I did not sub-cut the block on the top right since it looked small enough.

You may stop cutting here or make one more cut in some of the rectangles, perpendicular to the previous cut. In this step, I cut just two of the blocks.

We are done cutting. Each rectangle/square above is a stack of 6 fabric. Next step is to arrange the fabric within these rectangles.

Leave stack 1 alone with no change. For stack 2, move the fabric in top to the bottom of the stack. For stack 3, move the top two fabrics to the bottom. For stack 4, move the top three fabrics to the bottom. Likewise for stacks 5 and 6. Since we only have 6 fabrics in the stack, the fabrics for stacks 7, 8 and 9 will repeat and they will be similar to stacks 1,2 and 3, respectively. When all stacks are rearranged, this is what they look like:

Now we are ready to join the rectangles into pieced blocks.

From the 1″ solid strips, sub-cut a strip approximately as long as the bottom edge of rectangle 7. Sew it to rectangle 7, right sides together with a 1/4″ seam. Press towards the solid strip. Sew rectangle 9 to the other side of the solid strip.

You will put the block back together in exactly the reverse order in which you made the cuts. Use the 1″ solid sashing between rectangles.

Repeat for all the fabrics in the stacks. Make sure you keep the order of the fabric in the stacks. Here are all 6 pieced blocks.

Sandra,Thank you for visiting my blog and for your sweet comment. I have a post explaining orthogonal recursive bisection(ORB) which I will publish as soon as I get some pictures sorted out. It is a simple, common-sense algorithm as are most computer algorithms.Vasudha